I don't know if "gimp" has 2D FFT capabilities, but there must be some open source package that does. Take some circles, hyperbolae, etc., compute, and look at the 2D FFT's. The graphics/image processing/lens design communities have done a huge amount of work w/2D FFT's. In fact, if you stand right up against a lens, you effectively see the 2D Fourier transform of the image. It's a little distorted, but it's there. At 12:00 PM 3/23/2012, James Propp wrote:

Most responses to my post have focussed on the frequency-domain, but what about the specific patterns (circles, hyperbolas, etc.) that we see in the spatial-domain? At some point these need to be explained.

In fact, even leaving aside sunflowers, I'd like to see a nice mathematical explanation of Moire patterns of the conventional kind. Has such a thing ever been written? You'd think so, but I wasn't able to find one anywhere on the web last time I checked!

Jim Propp